Electrical machines can generally be operated in either a motoring mode, in which the machine converts an input of electrical energy to mechanical output such as force or torque, or in a generating mode, in which the machine converts an input of mechanical energy to an electrical output, such as current. In both cases, the output can have a time-varying component, which may be due to the input to the machine, the physical design of the machine or imperfections in the construction of the machine such as mechanical or magnetic asymmetry. For example, a brushless direct current (DC) machine operating as a motor may have a ripple component in its output torque which is due to time variations on the DC link supplying the machine, due to the dimensions of the slots in the stator laminations, due to the strengths and positions of the magnets on the rotor, due to manufacturing variance such as issues with encoder positioning, or due to a combination of these.
Much effort has been invested in methods of reducing the time or angle-varying components, particularly in reducing torque ripple in the output of a motor. With sufficient knowledge of the machine, it is possible to calculate current waveforms (also known as current profiles, that is phase currents for each phase specified as a function of rotor angle or time for a given torque demand) which would deliver smooth torque. However, such profiles are typically very sensitive to errors in the signal which describes the angular position of the rotor with respect to the stator, i.e. so-called angle error. Mathematically, this sensitivity is termed the solution sensitivity. A zero sensitivity solution is one which is minimally affected by angle error. For the avoidance of doubt, angle error may be caused by, for example, measurement errors, estimation errors, or discretisation errors due to the way in which the current control law is specified at a limited number of angles, e.g. in a lookup table with or without interpolation).
Prior art methods for reducing output ripple exist, as will now be described.
For example, there are methods which seek to reduce the angle error at source, e.g. by the use of very accurate encoders or resolvers to measure rotor position. These can be effective, but typically are very expensive (the cost of the transducer sometimes approaching the cost of the machine itself) and require precision alignment to the rotor. For mass-production drives, they are not a cost-effective solution. In addition, the rotor position sensor will exhibit errors over the rotation of the motor, particularly in the case of the low cost solutions which may, for example, be required in power steering applications.
Other examples are methods which address the voltage applied (and hence the current supplied) to the machine. Most of these methods take no account of the problem of angle error, so while they appear to provide a workable solution, in practice they are very variable in their effectiveness, since the angle error is unpredictable from drive to drive. For example, the paper “Computer-optimised smooth-torque current waveforms switched reluctance motors” by Lovatt and Stephenson, IEE Proceedings, Electric Power Applications, Vol 144, No 5, September 1997, pp 310-316 presents a method of determining current waveforms, but does not address the problem of errors in the angular information being used in the solutions.
There have been attempts to combine considerations of angular error and applied voltage. For example, U.S. Pat. No. 6,756,757 teaches how to calculate current profiles which result in smooth torque and which also have the property of zero (angle) sensitivity. However, the inventors have realised that this method is limited in that, while the phase currents can be specified in a way to achieve motor operation for a given operating point of speed and torque demand, these currents may require a range of DC link voltages which is not within the capability of the drive system. There are many applications in industry where there is a need to produce a machine output which (a) is not sensitive to angle error, (b) is able to accommodate limits on or variations of the DC link, (c) is not sensitive to manufacturing variations and (d) gives a smooth output.
There is therefore a need for a method of reducing output ripple in an electrical machine which takes account of the limitations of the available DC link voltage and the quality of the signal which describes the rotor position.